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In Figure, if PQ ST, PQR = 110° and RST = 130°, find QRS.

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In Figure, if PQ ST, PQR = 110° and RST = 130°, find QRS.

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First, construct a line XY parallel to PQ.

We know that the angles on the same side of transversal is equal to 180°.

PQR + QRX = 180°

QRX = 180°-110°

∴ QRX = 70°

Similarly,

RST + SRY = 180°

SRY = 180°- 130°

∴ SRY = 50°

Now, for the linear pairs on the line XY

QRX + QRS + SRY = 180°

Putting their respective values, we get,

QRS = 180° – 70° – 50°

Hence, QRS = 60°

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